Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;


public class A_Funky_Numbers {
	static long d; static int n;
public static void main(String[] args) {
	Scanner sc =  new Scanner(System.in);
     n=sc.nextInt();
     long a[]=new long[10000000];
     for (int i =1; i <=Math.sqrt(1e+9)*2; i++) {
		a[i]=((long)i*(i+1))/2;
	}
     for (int i = 1; i <=Math.sqrt(n)*2; i++) {
		d=n-a[i];
		long y=search(i,d,a,Math.sqrt(n)*2);
		if(y==1){
			System.out.println("YES");
			return;
		}
	}
     System.out.println("NO");
}
private static int search(int k, long d2, long[] c, double t) {
            int left=k;
            int right=(int)t;
            while(left<=right){
            	if(c[(left+right)/2]==d2)
            		return 1;
            	if(c[(left+right)/2]<d2)
            		left=(left+right)/2+1;
            	else
            		right=(left+right)/2-1;
            }
            return -1;
}
}